Contribution to the improvement of the QUICK scheme for the resolution of the convection–diffusion problems

The present paper deals with the improvement of a QUICK scheme for the resolution of convection–diffusion problems. In order to avoid any unstability problems and to increase the convergence speed a new deferred correction is suggested. Checking the required stability criteria, benefits are taken from the accuracy of the central difference scheme when it is possible. Otherwise, a upwind scheme is introduced in the deferred correction term warranting the stability of the whole scheme. Tests have been carried out on a wall driven square cavity and on a buoyancy driven cavity. Comparisons have been achieved with reference data in order to assess the accuracy of the present scheme. Further comparison with other differentiation scheme demonstrate that the present formulation is fast and accurate.